Tax Brackets

Progressive taxation: income is taxed at higher rates as more is earned

• The first dollar earned is taxed less than the last dollar earned.

• Marginal tax rate refers to the tax rate owed on next dollar you earn.

Tax Brackets

Deductions shield income from taxation

• Some retirement savings are tax-deductible

• Standard deductions vs. itemized deductions

  • Single filer: $12,950
  • Married filing jointly: $25,900

• Itemized deductions

  • Mortgage interest
  • State and local taxes (SALT)
  • Charitable contributions

General schedule

Gross Income

-Tax-Deductible Savings Contributions

-Other Deductible Items

=Adjusted Gross Income (AGI)

-Standard or Itemized Deduction

=Taxable Income

• Tax is calculated based on taxable income and filing status

Example

• Consider a single investor earning $65,000 per year.
  
• Assume they take the standard deduction of $12,590.
• Under the 2022 tax rates & brackets, what is the investor’s tax bill if they do not have any other deductions?
• What is the investor’s tax bill if they have contributed $6,000 to a traditional IRA?

Taxes and investments

• Investments are made in the hopes of generating income or price appreciation.
  
• The source of the return can impact the taxes owed.
• Interest income is taxed at ordinary income rates.
• Capital gains are taxed at different capital gains rates.
  • Is holding period short- or long-term?
  • Limits on deductibility of capital losses
  • Gain is calculated relative to your cost basis

2022 LT capital gains rates

Our benchmark

• We will explore how account taxation can affect the future value of investments.
• Our benchmark will be an investment with no tax advantages in which any gains are taxed immediately at ordinary income rates.

Some terminology and assumptions

We will assume 2 sets of tax rates:

1. Ordinary income rates \(\tau_{oi}\)
2. Capital gains rates \(\tau_{cg}\).

• We will assume constant tax rates from time \(t=0\) to time \(t=T-1\) before changing to new rates at time \(T\)
  • individual’s tax brackets may change in somewhat predictable ways
• 4 possible tax rates: \(\tau_{oi,0}\), \(\tau_{oi,T}\), \(\tau_{cg,0}\), \(\tau_{cg,T}\).

Tax Treatment #1

• No tax benefits
• Gains are taxed immediately at ordinary income rates

Tax treatment #2

• Non-deductible IRA
• Contributions are in after-tax dollars
• Taxation on gains is deferred until withdrawal at which time they are taxed as ordinary income

Tax treatment #3

• Non-dividend stock
• Investment made with after-tax dollars
• Taxation on gains is deferred until sale at which time they are taxed as capital gains

Tax treatment #4

• Roth IRA or a 529 college savings plan
• Contributions are made using after-tax dollars and earnings are tax-exempt

Tax treatment #5

• Traditional IRA or 401(k)/403(b) retirement plan.
• Contributions are made using pre-tax dollars (that is, contributions are tax deductible)
• Earnings are tax-deferred \(\rightarrow\) withdrawals taxed at ordinary income rates
  • withdrawals of both initial investment and gains

Tax treatment #5 (cont’d)

• Because the contribution is tax deductible, you save \(\tau_{oi,0}\) of taxes that would have otherwise been paid.
• The after-tax cost upon contribution is thus \(1-\tau_{oi,0}.\)
• The investment account grows to a time \(T\) value of \(\Pi_{t=1}^T \left(1+r_t\right)\) which is all taxed at withdrawal generating an after-tax time \(T\) value of \((1-\tau_{oi,T})\Pi_{t=1}^T \left(1+r_t\right)\).

Tax treatment #5 (cont’d)

After-tax return (after-tax FV/after-tax contribution): \[FV_5 = \frac{(1-\tau_{oi,T})\Pi_{t=1}^T \left(1+r_t\right)}{1-\tau_{oi,0}}\]

Traditional vs. Roth IRAs

If \(\tau_{oi,0}=\tau_{oi,T}\), traditional and Roth IRAs are equivalent on an after-tax basis.

• Roth IRAs are preferred if an investor’s tax rate is expected to be higher at withdrawal.
  • Better to pay taxes at low rate today
• Traditional IRAs are preferred if an investor’s tax rate is expected to be lower at withdrawl.
  • Better to shield taxes at high rate today

Asset location vs. asset allocation

Asset allocation: the choice of how much of each asset to hold

Asset location: the choice of where to locate different asset classes if different tax-advantaged accounts are available.

• This is a challenging problem!

• Investors with different expected tax rates may come to different allocation and location decisions.

• Rule of thumb: Hold more heavily taxed assets (corporate and Treasury bonds) in tax-deferred accounts and lightly-taxed assets (stocks) in taxable accounts

Mortgages

• For households, mortgage interest is tax-deductible, up to some limits.
  • Deduction reduces taxable income
  • Tax savings is: \[\tau_{\text{marginal}} \cdot \text{Deductible Mortgage Interest}\]

2022 tax year

• Mortgage interest expense on principal up to $750,000 is tax deductible.
• Taxpayer must itemize deductions rather than take the standard deduction
  • Single filer: $12,950
  • Married filing jointly: $25,900

Example

• The annual interest expense for a $500,000 mortgage with a 5% interest rate is $24,832.47 in the first year.
• For an investor with a 24% marginal tax rate and a $12,950 standard deduction, what is the incremental value of itemizing deductions?

Municipal Bonds

• Municipal bonds: issued by states and municipalities
• In an investor’s home state, muni coupons and original issue discount (OID) are exempt from state income tax
  • US treasury bonds are also exempt from state and local taxes
• Some munis qualify as exempt from federal income tax
• Munis are tax-exempt only at issuance

Muni yields

• Munis are primarily held by individuals (in the issuing state)
• These investors accept a lower yield than they would for a comparable taxable bond.

ETFs versus mutual funds

• ETFs are generally more tax-efficient than mutual funds.
• Flows in and out of mutual funds may generate sales of underlying assets in the mutual fund.
  • Resulting capital gains are passed on to the fund investor
• ETF investors thus are able to substantially defer capital gains taxation

Roth IRAs and skewed returns

• Withdrawals from Roth IRAs do not incur any tax.
• This tax treatment can be extraordinarily valuable for highly skewed assets.
• A famous example is Peter Thiel (PayPal founder and venture capitalist)
• Thiel’s Roth IRA is over $5 billion!
• Congress will likely cap the maximum balance that will be tax-free
• Paying attention to taxes pays…sometimes big!